Chapter 6: Income Redistribution
If the government actively pursues a policy
of equitable distribution, what is
considered equitable?
As always, EQUITY and EFFICIENCY are
the two conflicting issues the government
deals with.
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Chapter 6: Income Redistribution
History of Income Distribution
Rationales for Income
Redistribution
Cash vs. In-Kind Transfers
Overview
History - Income Distribution
In 2008:
The poorest 20% of the population received 4%
of before-tax income
The poorest 60% received 29% of before-tax
income
This is represented in the LORENZ CURVE,
where a 45% line represents equal income
distribution
Note that income inequality has increases slightly
since 1980.
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86e01310
4
Lorenz Evaluation
-Between 1980 and 2008, income share of the
top 20% increased, and income share of all
other quintiles decreased
-often blamed on globalization and welfare
cutbacks
-But similar changes occurred between 1961 and
1991, when welfare programs expanded and
there was economic growth
-this increase in income inequality may just be
temporary
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Theory - The Poverty Line
POVERTY LINE -real income needed to provide
a minimally adequate standard of living
-Statistics Canada instead uses Low Income
Cut-Off-Lines (LICO) where a family would
use 54.7% of its income on food, clothing, and
shelter as defined by 1992 expenditure
patterns
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History - The Poverty Line
The 2008 Low Income Cut-Off line for an
unattached individual was:
$22,171 for an in a 500,000 or greater urban area
$15,562 in a rural area
The 2008 LICO line for a family of 4 was:
$41,198 for an in a 500,000 or greater urban area
$28,361 in a rural area
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The Poverty Line
-The next graph shows Canadians below the cutoff line over time from 1980 to 2004
-note that poverty figures followed income figures
and the recession
-note that the statistics for children living in low
income is above average
-note that although overall the elderly living in
poverty has decreased, 33.7% of elderly
peoples living alone in 2008 lived in poverty
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The Poverty Line
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History - Poverty By Province
2008 poverty varies across Canada, from 9.1% of
families in Alberta to 16% of families in Quebec
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Poverty By Province
-35.1% half single-mother families are below the
poverty line (improved from 2005), and single
father families fare worse than two-parent
families
-a second paycheque is often required for a
“reasonable” standard of living
-stay-at-home parents have a disadvantage
-unfortunately, studies show that stay-athome parents have a huge positive effect on
their children, especially in early years
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Theory - Calculation Difficulties
All these numbers don’t take into account
IN-KIND income
-When a household member does work
(childcare, housecleaning, roof shoveling, tax
filing, plumbing, etc), it is not counted as
income
-If these activities were paid for, they would
appear as income
-Single parent households therefore have a lower
income (in-kind or reported)
-Stay at home parents have a higher true income
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than reported
Further Issues
-all the above data is before-tax, and therefore
doesn`t consider higher taxes for higher
incomes
-keep in mind that a person $1 below the poverty
line is treated the same as someone $10,000
below the poverty line in this chart
GAP RATIO =(Income-LICO)/LICO
-the aggregate low income gap ratio has
decreased to 33% in 2008 from 35% in 1980
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Theory – Family Categories
-Statistics Canada lists a household as “a group
of individuals sharing a common dwelling and
related by blood, marriage (including
common-law) or adoption
-Anyone else is considered (such as someone
with unrelated roomates) an “unattached
individual”
-2008 unattached individual income was $36,800,
and family income was $89,700
-The average family had 3 people
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Family Categories
-Families have savings in consumption
(especially the consumption of housing)
-Statistics Canada considers a second adult of a
family unit to increase household needs by
40%, and each child to increase household
needs by 30%
-Therefore the average family has needs of 1.7
unattached individuals. A family receiving
$89,700 thus has the equivalent unattached
individual income of $52,764
-This is arbitrary, but argues the average 315
person family is better off
Theory – Data and Distribution
-Typical income data is yearly, which is not
perfect, as income tends between years
(person A may have a higher income due to
being older than person B)
-Income distribution in Canada has varied little
since 1951
-This is odd, since social programs increased
greatly after WWII
-perhaps preventing a huge income shift?
-could have further programs done more?
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Family Data
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Theory - Poverty Conclusion
-EXACT income inequality sources are highly
studied and still debated
-Studies show family income inequality comes
from differences in wages and salaries for
family heads
BUT
-Property income (interest and dividends)
accounts for little of the inequality
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Theory - Poverty Conclusion
WHY different wages?
Wage = f(strength, intelligence, effort, education,
marriage decisions, discrimination, welfare,
luck)
-computer technology is making education a huge
factor of wage,
-BUT DOESN’T EXPLAIN EVERYTHING
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Theory - Rationales for Income Redistribution
There are a variety of rationales for income
redistribution, all requiring unique
underlying assumptions:
1) Utilitarianism
2) The Maxmin Criterion
3) Pareto Efficient Income Redistribution
(Insurance and Alturism)
4) Nonindividualistic Views
5) Other (ie: Fairness/Good Rules, etc)
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1) Theory - Utilitarianism
-Social welfare is a function of undividual
utility:
W=F(U1, U2,…,Un)
-Certain utilitarianism philosophers
(Bentham and Mill) argued that public
policies should be guided by the
principle, “greatest good for the greatest
number"
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Utilitarianism
-Economists typically interpret this idea
through an additive social welfare
function:
W=U1+U2+…+Un
-The utilitarian therefore supports income
distribution as long as it increases social
welfare
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Utilitarianism Assumptions
-In order to take this analysis further, one
needs to add 3 assumptions:
1) Individuals have identical utility functions
only depending on income U=f(I)
2) Diminishing marginal utility of income
exists
3) Total societal income is fixed
-Therefore welfare is maximized when
incomes are completely equal:
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Utilitarian Example
Consider a society with two people, Richard
(who starts rich) and Po (who starts poor).
Graphically, our x axis can represent the entire
income available in society (assumption 3)
Richard and Po’s marginal utilities are measured
along opposite sides, as they are both
functions of income, and both diminishing due
to assumption 2
-They are symmetrical due to assumption 1
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MUR
O
MUP
x
Richard’s
income is Ox,
and Po’s income
is O’x.
O’
The distribution expressed by point x (Richard is richer
than Po) implies a high MU for Po and a low MU for
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Richard.
Utilitarian Example
Redistribution of income makes one person
worse off and another better off
-The change in utility is expressed by the area
under the utility curve
-we see that if Richard gives money to Po, Po’s
gained utility is greater than Richard’s lost
utility, resulting in higher social welfare
-social welfare is thus maximized at I, where both
people have half the available income
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MUR
MUP
s
r
t
v
O
I w
x
If income
moved from x to
w, Richard
would lose
utility tvxw
while Po would
gain utility rsxw.
O’
Society’s gain would therefore be rsvt. Social welfare
would be maximized at point I.
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Utilitarian Criticism
-This result seems too easy – society is
best off if everyone has EXACTLY the
same income
In order to evaluate this result, we have to
look back to Utilitarianism’s underlying
assumptions
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Utilitarian Assumption 1
We can’t ACTUALLY measure utility, nor can we
determine if people have identical utility
functions. However:
1) It seems reasonable
-If people are similar in other characteristics
(height, weight, etc.), why not utility?
2) It should be so (ethics)
-Perhaps government should act according to
identical utility functions, to avoid bias
ASSUMPTION 1 IS WEAK, BUT MAY SURVIVE
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Utilitarian Assumption 2
We can prove diminishing marginal utility of a
GOOD, but not of INCOME
-Perhaps someone can keep spending
income on different things to keep his
marginal utility high
If Marginal Utility is constant, then a dollar taken
away from Richard causes a decrease in
utility equal to the utility gained by Po
ASSUMPTION 2 FAILS?
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Utilitarian Assumption 3
People typically gain utility from leisure, and
therefore transfers discourage work and
cause a reduction in overall income
-Therefore each dollar transfer causes a
reduction in available income
-If we aim for a 50%/50% balance, this balance
suddenly becomes unequal as perhaps only
90% of the income is now available (so the
balance becomes 50%/40%)
ASSUMPTION 3 IS PROBLEMATIC
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Utilitarian Social Welfare
45* Line
Maka’s Utility
In Utilitarianism, Social
Indifference Curves are
straight lines
O
Maka
i
iii
With no tax
distortion, point
ii is optimal
ii
W``
W`
With tax
distortions,
point iii is
optimal
Susan’s Utility
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2) Theory - The Maxmin Criterion
-if the social objective is the maximin criterion,
society attempts to maximize the utility of the
least well-off person:
W=min(U1, U2,…,Un)
-This claims that society is only as well off as its
“worst” member
-There is an implicit argument for equality, but
income variance is still allowed for
-ie: don’t overtax the rich to pay the poor if it
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makes the poor lose their jobs
Maxmin Social Welfare
45* Line
Maka’s Utility
Social Indifference Curves
are right angles
O
Maka
i
ii
iv
W``
W`
With no tax
distortion, point
ii is optimal
With tax
distortions,
point iv is
optimal
Susan’s Utility
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Maxmin vs. Utilitarian Social Welfare
45* Line
Maka’s Utility
With no distortion, the
results are identical
O
Maka
i
With tax distortion,
maxmin theory argues
for more redistribution
thus higher inefficiency
iii
ii
iv
W``
W`
Susan’s Utility
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The Maxmin Criterion Criticism
-this is based on John Rawls’(1971) idea of an
ORIGINAL POSITION
-theoretically, if people didn’t know their place
in society, they would want the lowest place to
be as well-off as possible
-this assumes everyone is VERY risk
adverse
-Feldstein (1976) also points out that this
condition allows for policies creating a few
extreme rich and penalizing most of society as
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long as the poorest gains slightly
3) Theory – Pareto Efficient
Income Redistribution
Utilitarian and maxmin models do NOT provide
Pareto Efficient Income redistribution
-one person is made WORSE OFF (lose
income)
Income Redistribution can be a Pareto
Improvement under concepts of:
a) Altruism
b) Insurance
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3a) Theory - Altruism
-Due to altruism, Richard may GAIN utility from
giving money to Po (a Pareto improvement)
-ideal redistribution would continue until Richard’s
Marginal Utility gain from altruism equals his
Marginal Utility loss from lower income
-one may argue that the government can find the
poor easier than Richard can
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Altruism
-taken to the extreme, income distribution
becomes a PUBLIC GOOD, because
everyone gains utility from knowing the poor
are taken care of
-the free-rider problem argues for the
government forcing redistribution payments
(people will naturally wait someone else to
take care of the poor)
-Many argue that people don’t need the
government to redistribute their money, they
could do it if they wanted
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3b) Insurance
-many have self-interest reasons for favoring
insurance
-Income redistribution payments are
premiums against the risk of becoming poor
-Additionally, income redistribution is insurance
against civil unrest
-give the poor food so they don’t become
Robin Hood
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4) Theory - Nonindividualistic Views
-Thus far we have argued that redistribution
policy should come from the social welfare
function
-Some argue that social redistribution should be
independent from individual tastes
-Fair (1971) pointed out that Plato argued that
in a good society: Income
Richest
IncomePoorest
4
-Others simply argue that equal distribution is
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paramount
5) Theory – Other/Fairness
-the previous models assumed that society
should distribute ITS income as it sees fit
-(assumes people don’t own income)
-one could examine the FAIRNESS of initial
income earning or income redistribution
-should EQUAL OPPORTUNITY be the goal,
regardless of the income distribution that
results?
-in this case there would be no room for
government redistribution
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Other/Good Rules
-Nozick (1974) argues that income belongs to
individuals, and government should ensure
“good” sets of rules to govern society’s
operation, not “good” income distribution
-But how can one evaluate “good” rules
without examining income distribution?
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Other/Fairness (another look)
-others argue that social mobility is paramount
-it doesn’t matter if people are poor now, as
long as there is a decent chance of their
situation changing
-Chen (2009) showed that:
1) 70% of Canadians moved to another decile
group in 5 years and
2) 30-40% moved UP at least one decile
Note: decile groups (11-20%,41-50%, 91-100% etc)
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Cash vs. In-Kind Transfers
Thus far we have assumed income is
redistributed in the form of cash transfers
-Often the poor receive in-kind transfers (food,
education, healthcare, etc)
-There are a variety of pro’s and con’s when
comparing cash to in-kind transfers:
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Composite good, units
Example: Consider a situation where
an individual consumes Fa food, yet the
government considers the minimum
food an individual needs as Fmin.
Maximum food consumption is I/Pf
I
A
FA
FMin
I/Pf
Food (units)
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Composite good, units
One option is to offer a food
voucher FV, increasing utility
and consumption to point B.
I
•
A
•
Note that non-food
consumption also increases
slightly
B
Food
FA
FV FMin
I/Ph
I/(1-s)Ph 47
Composite good, units
Without the subsidy, C2 is the
level of consumption that
could be undertook at the
minimum food consumption.
I
•
V
A
•
Therefore V is the cost of the
food subsidy
B
C2
Food
FA
FV FMin
I/Ph
I/(1-s)Ph 48
Composite good, units
An alternative to the subsidy
would therefore be a lumpsum transfer.
In THIS case, the outcome is
the same
I
•
V
A
•
B
C2
Food
FA
FV FMin
I/Ph
I/(1-s)Ph 49
Composite good, units
•
I
•
V
A
•
B
Depending on the utility
function, the individual
COULD use some or all of the
cash transfer on composite
goods rather than food,
achieving higher utility
C2
Food
FA
FV FMin
I/Ph
I/(1-s)Ph 50
Cash vs. In-Kind Transfers
Cash transfers:
1) give a higher level of utility
-(people are happier)
2) are more highly valued (Whitmore 2002
estimated food voucher value as 80 cents per
dollar)
3) have lower administration costs
-Blanchard (1982) estimated that US food
stamp administration costs would be reduced
by 36% through a move to a cash transfer
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Theory – Why In-Kind Transfers?
If lump-sum cash transfers seem so preferred
and efficient, why are in-kind transfers so
common?
1) Asymmetric Information
2) Commodity Equalitarianism
3) Paternalism
4) Politics
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1) Asymmetric Info
Asymmetric information can argue for in-kind
transfers:
-with asymmetric information, people who are not
poor or in need may claim to be poor or in
need to get a free handout
-in this case, in-kind transfers may screen the
truly needy from the truly greedy
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1) Asymmetric Info
Assume we have two people, Muscles, who is in
great shape, and Payne, who has an injured
shoulder. We have the scenario:
UM= CM+H
UP=CP+hT
R=CM+CB+T
Where C=consumption
H=base utility from being healthy
h=marginal utility of therapy
T=expenditure on therapy
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R=society resources
Full information gives this utility
possibilities curve coming from all
possible income transfers.
UP
R
Note that utility
is equal along the
45* line
(R+H)/2
45*
H
(R-H)/2
R+H
UM
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At a, Payne receives all income,
and Muscles just gains utility from
his health
At b, utilities are equal,
but Payne receives
more money to make
b
up for his injury
c
UP
a
R
(R+H)/2
R/2
45*
d
H
(R-H)/2
R/2+H
R+H
UM
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At c, income is equal, thus Payne
has a lower utility due to his injury
UP
a
R
At d, Muscles gets all
income and Payne’s
utility is zero
b
(R+H)/2
R/2
c
45*
d
H
(R-H)/2
R/2+H
R+H
UM
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A maxmin theorem would perfer
b, and a Utilitarian would be
indifferent along ad.
Under full information,
no vouchers are
required, only a cash
b
transfer
c
UP
a
R
(R+H)/2
R/2
45*
d
H
(R-H)/2
R/2+H
R+H
UM
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With Asymmetric information, the
most that Payne could receive
would be R/2, else muscles would
pretend to be injured for the
subsidy
Note that the
utility
c
possibilities
curve has
decreased to cd
UP
R
(R+H)/2
R/2
45*
d
H
(R-H)/2
R/2+H
R+H
UM
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In-Kind Transfers w/Asymmetric Info
If the marginal utility of therapy>0.5, in-kind
transfers could alleviate this problem.
If society taxes each person 50 cents, and then
gives $1 to Payne, if his MU of therapy is
greater than 0.5 (greater than his tax), this
increases his utility
This creates a kink in the utility possibilities curve
with the slope 1-2h
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With in-kind transfers, the utility
possibilities curve is improved to
gcd
A maxmin theory
would prefer point e,
and a utilitarian
would prefer a point
along cd
c
e
UP
R
g
(R+H)/2
R/2
45*
d
H
(R+H)/2
R/2+H
R+H
UM
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Cash & In-Kind Transfers w/Asymmetric Info
Note that the optimal point along any of the above
utility possibilities curve depends on the
indifference curve derived from the social
welfare function W=f(UM,UP)
-This proves, however, that because a noninjured person wouldn’t want therapy, in-kind
transfers reduce the incentive to fake an injury
under asymmetric information
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2) Commodity Egalitarianism
Commodity Egalitarianism claims that
commodities should be distributed equally
-This makes sense for some commodities:
ie: right to vote, basic foodstuffs, clean water
-This is problematic for other commodities:
Ie: healthcare (should sick and well get same
care?), primary school (should smart and
average children get same resources), video
games (should people who don’t play video
games still get them?)
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3) Paternalism
If someone has a paternalistic attitude towards
the sick or poor, their utility increases when
the sick or poor consume certain commodities
(such as healthcare, or food or shelter)
-This is a type of positive externality
-Note that this often doesn’t apply to all
commodities (ie: cigarettes or beer)
-an In-Kind transfer ensures the commodity in
question is consumed, thus dealing with the
positive externality
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4) Politics
In-Kind transfers also have the advantage of
increasing the demand for the commodity in
question (food, housing, etc)
Also the public employees overseeing the
transfers are given jobs, reducing
unemployment
-This can have a good effect on the economy
-And therefore a positive political effect for the
politician proposing it
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Income Transfer Overview
Most people agree that the government should be
involved in income transfer
-But often disagree as to the perfect
distribution of income
-Due to asymmetric information, any lump-sum
change must focus on income and therefore
becomes a distortionary income tax
-In-kind transfers are less efficient than lump-sum
transfers….
-but are used due to asymmetric information,
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commodity egalitarianism, paternalism & politics
Chapter 6 Summary
 Utilitarians argue that income should be split
equally, which requires:
1) W=∑U, with all U’s equal
2) Decreasing MU of income
3) Fixed total income
-since these assumptions (especially 3) are
problematic, income redistribution is more
difficult
 The maxmin criterion seeks to raise the utility
of the worst off person
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-this has issues (often allows for odd results)
Chapter 6 Summary
 Income redistribution may a Pareto
Improvement or a public good, if people gain
utility from equity
 Other theories abound on what goods should
be distributed equally and what a “fair”
distribution is
 Income is hard to measure correctly
 In-kind transfers have efficiency
disadvantages
 But other significant advantages
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